Silvio Capobianco ; Jarkko Kari ; Siamak Taati - Post-surjectivity and balancedness of cellular automata over groups

dmtcs:1485 - Discrete Mathematics & Theoretical Computer Science, September 15, 2017, Vol. 19 no. 3 - https://doi.org/10.23638/DMTCS-19-3-4
Post-surjectivity and balancedness of cellular automata over groups

Authors: Silvio Capobianco ; Jarkko Kari ; Siamak Taati

    We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.


    Volume: Vol. 19 no. 3
    Section: Automata, Logic and Semantics
    Published on: September 15, 2017
    Accepted on: September 15, 2017
    Submitted on: July 18, 2017
    Keywords: Mathematics - Dynamical Systems,Nonlinear Sciences - Cellular Automata and Lattice Gases,37B15, 68Q80, 37B10

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